Lipschitz Invariance of Critical Exponents on Besov Spaces

Year:    2020

Author:    Qingsong Gu, Hui Rao

Analysis in Theory and Applications, Vol. 36 (2020), Iss. 4 : pp. 457–467

Abstract

In this paper we prove that the critical exponents of Besov spaces on a compact set possessing an Ahlfors regular measure is an invariant under Lipschitz transforms. Under mild conditions, the critical exponent of Besov spaces of certain self-similar sets coincides with the walk dimension, which plays an important role in the analysis on fractals. As an application, we show examples having different critical exponents are not Lipschitz equivalent.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-SU5

Analysis in Theory and Applications, Vol. 36 (2020), Iss. 4 : pp. 457–467

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

Keywords:    Lipschitz invariant Besov space critical exponents walk dimension heat kernel.

Author Details

Qingsong Gu

Hui Rao